Games like AmaZoo
Games like AmaZoo include Baba Is You, Zup! S, Patrick's Parabox, Pikuniku, and Scribblenauts Unlimited. We matched them by the tags players give AmaZoo on Steam (Singleplayer, Puzzle, 2D, Sokoban, and Grid-Based Movement): closest matches first, and among equally close ones the better-known games.

Baba Is You
Shared: Puzzle · Singleplayer · Sokoban

Zup! S
Shared: Puzzle · 2D · Casual

Patrick's Parabox
Shared: Puzzle · Sokoban · Singleplayer

Pikuniku
Shared: Puzzle · Casual · Cute

Scribblenauts Unlimited
Shared: Puzzle · Singleplayer · Casual

Strange Jigsaws
Shared: Puzzle · 2D · Casual

Cat Goes Fishing
Shared: 2D · Singleplayer · Cute

OneShot
Shared: Puzzle · Singleplayer · Cute

Is This Seat Taken?
Shared: Puzzle · Casual · Singleplayer

Gorogoa
Shared: Puzzle · Singleplayer · Casual

A Little to the Left
Shared: Puzzle · Singleplayer · Casual

Slime Rancher
Shared: Singleplayer · Cute · Adventure

Plants vs. Zombies GOTY Edition
Shared: Singleplayer · Casual · 2D

There Is No Game: Wrong Dimension
Shared: Puzzle · Singleplayer · Indie

Carto
Shared: Puzzle · Cute · Singleplayer

World of Goo
Shared: Puzzle · Singleplayer · 2D

Zup! 2
Shared: Puzzle · 2D · Casual

The Last Campfire
Shared: Puzzle · Singleplayer · Cute

Donut County
Shared: Puzzle · Casual · Cute

Void Stranger
Shared: Puzzle · Singleplayer · Sokoban

Chants of Sennaar
Shared: Puzzle · Singleplayer · Adventure

Snakebird
Shared: Puzzle · Singleplayer · 2D

Zup!
Shared: Puzzle · 2D · Casual

Changed
Shared: Puzzle · Singleplayer · Cute